### Coin-Die Experiment

 Coin Die0 Die1
Distribution graph

#### Description

The coin die experiment consists of first tossing a coin, and then rolling a red die if the coin lands head or a green die if the coin lands tails. Random variable $$X$$ gives the coin score (1 for heads and 0 for tails) and random variable $$Y$$ gives the die score. These random variables are recorded on each update in the data table. The probability distribution that governs the red die and the distribution that governs the green die can be specified with the select boxes; the choices are

• fair: each face has probability $$\frac{1}{6}$$.
• 1-6 flat: faces 1 and 6 have probability $$\frac{1}{4}$$ each; faces 2, 3, 4, and 5 have probability $$\frac{1}{8}$$ each.
• 2-5 flat: faces 2 and 5 have probability $$\frac{1}{4}$$ each; faces 1, 3, 4, and 6 have probability $$\frac{1}{8}$$ each.
• 3-4 flat: faces 3 and 4 have probability $$\frac{1}{4}$$ each; faces 1, 2, 5, and 6 have probability $$\frac{1}{8}$$ each.
• skewed left: face $$i$$ has probability $$\frac{i}{21}$$ for $$i \in \{1, 2, 3, 4, 5, 6\}$$.
• skewed right: face $$i$$ has probability $$\frac{7 - i}{21}$$ for $$i \in \{1, 2, 3, 4, 5, 6\}$$.

The probability of heads $$p$$ for the coin can be varied with a scroll bar. The probability density function and moments of $$Y$$ are shown in blue in the distribution graph and are recorded in the distribution table. On each update, the empirical density function and moments of $$Y$$ are shown in red in the distribution graph and are recorded in the distribution table.

This applet illustrates Conditional Probability and Conditional Distributions.